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A081204
Staircase on Pascal's triangle.
3
1, 2, 3, 10, 15, 56, 84, 330, 495, 2002, 3003, 12376, 18564, 77520, 116280, 490314, 735471, 3124550, 4686825, 20030010, 30045015, 129024480, 193536720, 834451800, 1251677700, 5414950296, 8122425444, 35240152720, 52860229080, 229911617056
OFFSET
0,2
COMMENTS
Arrange Pascal's triangle as a square array. This sequence is then a diagonal staircase on the square array.
LINKS
FORMULA
a(n) = binomial(ceiling((n)/2) + n, n).
a(n) = Sum_{k=0..floor(n/2)} binomial(n+k-1, k). - Paul Barry, Jul 06 2004
Conjecture: 4*n*(n+1)*(6*n^2 - 15*n + 8)*a(n) + 6*n*(9*n-7)*a(n-1) - 3*(3*n-4)*(3*n-2)*(6*n^2-3*n-1)*a(n-2) = 0. - R. J. Mathar, Nov 07 2014
Conjecture: 8*n^2*(n+1)*a(n) - 12*n*(83*n^2 - 313*n + 232)*a(n-1) + 6*(-9*n^3 - 377*n + 384)*a(n-2) + 9*(3*n-5)*(83*n-64)*(3*n-7)*a(n-3) = 0. - R. J. Mathar, Nov 07 2014
MATHEMATICA
Table[Binomial[Ceiling[(n)/2] + n, n], {n, 0, 30}] (* Vincenzo Librandi, Aug 07 2013 *)
PROG
(Magma) [Binomial(Ceiling((n)/2) + n, n): n in [0..30]]; // Vincenzo Librandi, Aug 07 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 11 2003
STATUS
approved